Transport Phenomena and Kinetic Theory (eBook)

Applications to Gases, Semiconductors, Photons, and Biological Systems

Carlo Cercignani, Ester Gabetta (Herausgeber)

eBook Download: PDF

2007 | 2007
XIII, 271 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4554-0 (ISBN)

Infos

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning.

 

Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

 

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This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex systems in various ?elds of applied sciences. Mathematical kinetic theory is essentially based on the Boltzmann eq- tion, which describes the evolution, possibly far from equilibrium, of a class of particles modelled as point masses. The equation de?nes the evolution in time and space of the distribution function over the possible microscopic states of the test particle, classically position and velocity. The test particle is subject to pair collisions with the ?eld particles. The interested reader can ?nd in the book, Theory and Application of the Boltzmann Equation, by C. Cercignani, R. Illner, and M. Pulvirenti, Springer, Heidelberg, 1993, all necessary knowledge of the physics and mathematical topics related to this celebrated model of non-equilibrium statistical mech- ics. Another important model of mathematical kinetic theory is the Vlasov equation, where interactions between particles are not speci?cally collisions, but mean ?eld actions of the ?eld particles over the test particle. The model de?nes again an evolution equation for the one-particle distribution function over the microscopic state of the test particle. The two models brie?y mentioned above can be regarded as the fun- mental models of mathematical kinetic theory and the essential background o?ered from the kinetic theory for classical particles towards the modelling of large systems of several particles undergoing non classical interactions.

Inhalt

Preface 6
Contents 10
List of Contributors 12
Part I Analytic Aspects of the Boltzmann Equation 15
1 Rigorous results for conservation equations and trend to equilibrium in space-inhomogeneous kinetic theory 16
2 Results on optimal rate of convergence to equilibrium for spatially homogeneous Maxwellian gases 31
3 Nonresonant velocity averaging and the Vlasov – Maxwell system 50
Part II Modeling Applications, Inverse and Computational Problems in Quantum Kinetic Theory 64
4 Multiband quantum transport models for semiconductor devices 65
5 Optimization models for semiconductor dopant profiling 100
6 Inverse problems for semiconductors: models and methods 125
7 Deterministic kinetic solvers for charged particle transport in semiconductor devices 158
Part III Miscellaneous Applications in Physics and Natural Sciences 179
8 Methods and tools of mathematical kinetic theory towards modelling complex biological systems 180
9 Kinetic modelling of late stages of phase separation 199
10 Ground states and dynamics of rotating Bose – Einstein condensates 219
11 Two inverse problems in photon transport theory: evaluation of a time- dependent source and of a time- dependent cross section 260

Produkt-Details

• Erscheint lt. Verlag: 3.12.2007
• Reihe/Serie: Modeling and Simulation in Science, Engineering and Technology
• Reihe/Serie: Modeling and Simulation in Science, Engineering and Technology
• Zusatzinfo: XIII, 271 p. 26 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Complex Systems • Mathematics • Modeling • Modelling • Natur • Optimization • Physics • Profil • Science • Transport
• ISBN-10: 0-8176-4554-3 / 0817645543
• ISBN-13: 978-0-8176-4554-0 / 9780817645540